Which ordered pairs make both inequalities true? Check all that apply. y < 5x + 2 y >= 1/2x + 1 These are the choices.... #1. (–3, 2) #2. (–1, 3) #3. (0, 2) #4. (1, 2) #5. (2, –1) #6. (2, 2) - QAmmunity.org

Which ordered pairs make both inequalities true? Check all that apply. y < 5x + 2 y >= 1/2x + 1 These are the choices.... #1. (–3, 2) #2. (–1, 3) #3. (0, 2) #4. (1, 2) #5. (2, –1) #6. (2, 2)

asked Sep 6, 2017 67.8k views

2 Answers

we have

y < 5x + 2 -------> inequality

$y \geq (1)/(2)x + 1$ -------> inequality

using a graph tool

see the the attached figure N

the solution of the system is the shaded area

This point satisfies the inequality
but does not satisfy the inequality
.

therefore

it is not a solution of the system

see the attached figure N

inequality

$(-3,2)\\ x=-3\\ y=2$

2 < 5*(-3) + 2

2 < -13 -----> is not true

inequality

$(-3,2)\\ x=-3\\ y=2$

$2 \geq (1)/(2)*(-3) + 1$

$2 \geq -(1)/(2)$ -----> is true

This point satisfies the inequality
but does not satisfy the inequality
.

therefore

it is not a solution of the system

see the attached figure N

inequality

$(-1, 3)\\ x=-1\\ y=3$

3 < 5*(-1) + 2

3 < -3 -----> is not true

inequality

$(-1, 3)\\ x=-1\\ y=3$

$3 \geq (1)/(2)*(-1) + 1$

$3 \geq (1)/(2)$ -----> is true

This point satisfies the inequality
but does not satisfy the inequality
.

therefore

it is not a solution of the system

see the attached figure N

inequality

$(0, 2)\\ x=0\\ y=2$

2 < 5*(0) + 2

2 < 2 -----> is not true

inequality

$(0, 2)\\ x=0\\ y=2$

$2 \geq (1)/(2)*(0) + 1$

$2 \geq 1$ -----> is true

This point satisfies the inequality
and satisfies the inequality
.

therefore

it is a solution of the system

see the attached figure N

inequality

$(1, 2)\\ x=1\\ y=2$

2 < 5*(1) + 2

2 < 7 -----> is true

inequality

$(1, 2)\\ x=1\\ y=2$

$2 \geq (1)/(2)*(1) + 1$

$2 \geq (3)/(2)$ -----> is true

This point satisfies the inequality
but does not satisfy the inequality
.

therefore

it not a solution of the system

see the attached figure N

inequality

$(2, -1)\\ x=2\\ y=-1$

-1 < 5*(2) + 2

-1 < 12 -----> is true

inequality

$(2, -1)\\ x=2\\ y=-1$

$-1 \geq (1)/(2)*(2) + 1$

$-1 \geq 2$ -----> is not true

This point satisfies the inequality
and satisfies the inequality
.

therefore

it is a solution of the system

see the attached figure N

inequality

$(2, 2)\\ x=2\\ y=2$

2 < 5*(2) + 2

2 < 12 -----> is true

inequality

$(2, 2)\\ x=2\\ y=2$

$2 \geq (1)/(2)*(2) + 1$

$2 \geq 2$ -----> is true

therefore

the answer is

$case 4) (1, 2)\\ case 6) (2, 2)$

Which ordered pairs make both inequalities true? Check all that apply. y < 5x + 2 y-example-1

Which ordered pairs make both inequalities true? Check all that apply. y < 5x + 2 y-example-2

Daan Wilmer answered Sep 8, 2017

7.3k points

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